Default correlation modelling is becoming the most popular problem in the
field of credit derivatives pricing. An increase in default risk would cause the
recovery rate to change correspondingly. Correlation between default and
recovery rates has a noticeable effect on risk measures and credit derivatives
pricing.
After an introduction, we review the most recent literature covering default
correlation and the relationship between default and recovery rates. We
adopt the copula methodology to focus on estimating the default correlations
rather than focus on modelling probabilities of default, we then use stress
testing to compare the distributions of the probability of default under different
copula functions. We develop a Gamma-Beta model to link the recovery
rate directly with the individual probability of default, this is instead of an
extended one factor model to relate them by a systematic common factor.
One factor models are re-examined to explore correlated recovery rates under
three distributions: the Logit-normal, the Normal and the Log-normal. By
analyzing the results respectively obtained from these two classes of modelling
scheme, we argue that the direct dependence (Gamma-Beta) model
behaves better, in estimating the recovery rate given individual probability
of default and in suggesting a better indication of their relationship. Finally,
we apply default correlation and the correlated recovery rate to portfolio risk
modelling. We conclude that if the recovery rates are independent stochastic
variables, the expected losses in a large portfolio might be underestimated
because the uncorrelated recovery risks can be diversified, so the correlation
between default rate and recovery risk can not be neglected in the applications.
Here, we believe the first time, the recovery rate depends on individual
default probability by means of a closed formula.